Natural circulation with two-phase flow is a nonlinear dynamical systems, which can show a very complex and strange behavior under specific conditions. The application of stability analysis requires a large computational effort and is cumbersome in case of prediction the dynamical behavior by system codes alone. Therefore, model order reduction techniques are used to compensate this disadvantage by coupling with a bifurcation code such as MatCont. A reduced order model is derived by employing the POD-method to analyze the stability landscape of a low pressure natural circulation system representing passive safety systems such as the containment cooling condenser. The required full order model contains a classical natural circulation loop with a heated section and a riser. The two-phase region is modeled by a drift-flux mixture model. The reliability of the FOM is investigated by comparison with a reference model by the validated system code ATHLET.